Parallel Lotteries: Insights from Alaskan Hunting Permit Allocation

We analyze the parallel lottery that is used to allocate hunting permits in the state of Alaska. Each participant is given tickets to distribute among lotteries for different types of items. Participants who win multiple items receive their favorite, and new winners are drawn from the lotteries with unclaimed items. When supply is scarce, equilibrium outcomes of parallel lotteries approximate a competitive equilibrium from equal incomes (CEEI), which is Pareto efficient. When supply is moderate, parallel lotteries exhibit two sources of inefficiency. First, some agents may benefit from trading probability shares. Second, outcomes may be “wasteful”: agents may receive nothing even if acceptable items remain unallocated. We bound both sources of inefficiency and show that each is eliminated by giving applicants a suitable number of tickets k: trades are never beneficial when k = 1, and waste is eliminated as [Formula: see text]. In addition, we show that the wastefulness of the k-ticket parallel lottery has some benefits: agents with strong preferences may prefer parallel lottery outcomes to those of any nonwasteful envy-free mechanism. These agents prefer small values of k, while agents with weak preferences prefer large values of k. Together, these results suggest that the k-ticket parallel lottery performs well under most circumstances and may be suitable for other settings where items are rationed. This paper was accepted by Gabriel Weintraub, revenue management and market analytics.

A Double-Weighted Bankruptcy Method to Allocate CO2 Emissions Permits

Global warming, as a result of greenhouse gases, is exceeding the planet’s temperature stabilization capacities. Thus, greenhouse gas emissions must be reduced. We analyse a bankruptcy situation aimed at allocating emissions permits of CO2, the predominant greenhouse gas emitted by human activities. Inspired by the Constrained Equal Awards (CEA) solution for bankruptcy situations, we introduce a new allocation protocol based on the extension of the CEA solution over double-weighted bankruptcy situations, including two exogenous parameters aimed at providing a balance, in the request of emissions permits, between economic activities and the production of renewable energy. In these bi-criteria allocation problems, we focus on a computational approach to find an allocation protocol that does not prioritize any particular parameter. As an application of our method, we first consider CO2 permit allocation problems in European Union (EU) countries, using real data about the gross domestic product (GDP), the production rate of renewable energies, and countries’ ‘demands’ of CO2 emissions from 2010 to 2014. Then, we compare our approach with the CEA solution and its single-weighted extension to show the impact of using two weights over the distribution of CO2 emissions permits; we analyse the correlation between allocations of CO2 emission permits and the distribution of power within the EU Council to study the acceptability of alternative allocations.

Market Power in Output and Emissions Trading

This article focuses on the strategic behavior of firms in the output and the emissions markets in the presence of market power. We consider the existence of a dominant firm in the permit market and different structures in the output market, including Cournot and two versions of the Stackelberg model, depending on whether the permit dominant firm is a leader or a follower in the output market. In all three models, the firm that dominates the permit market is more sensitive to its initial allocation than its competitor in terms of abatement and less sensitive in terms of output. In all three models, output is decreasing and the permit price is increasing in the permit dominant firm’s initial allocation. In the Cournot model, permit dominance is fruitless in terms of output and profit if the initial allocation is symmetric. Output leadership is more relevant than permit dominance since an output leader always tends to, ceteris paribus, produce more and make more profit whether it also dominates the permit market or not. This leadership can only be overcompensated for by distributing a larger share of permits to the output follower, and only if the total number of permits is large enough. In terms of welfare, Stackelberg is always superior to Cournot. If the initial permit allocation is symmetric, welfare is higher when the same firm dominates the output and the permit market at the same time.